Question

How do you calculate `log_2 (9)`?

Answer 1

Enter it into a calculator. It's about `3.17`.

Explanation:

You can change it around a bit, knowing that `9 = 3^2`, so

`log_2 9 = log_2 3^2 = 2log_2 3`, but this is a longer way to get to the same answer, and you still have to use a calculator, because you can't do `2^3.17` in your head, unless you have a heavy dosage of savant syndrome.

Have decimals in exponents doesn't seem correct. It actually makes more sense as a fraction,

`2^3.17 = 2^(317/100)`

which you can then turn into a root,

`2^(317/100) = root(100)2^317`

which is actually what is meant by `2^3.17`.